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# Making A Manoeuvre Burn Using Two Stages?

## Question

Something that's often puzzled me is if there's a calculation to figure out how long it will take to complete a manoeuvre if I need to use two separate stages to make the burn?

For example, my next mission sees me in orbit with a full tank with a Swivel engine.  The next stage has a NERV engine which isn't going to produce anything like the thrust of the Swivel.  Reading KER, it tells me my Swivel stage will run for (let's say) 1.20.  So what I was trying was to take the Delta V this stage would take from the total required to complete the manoeuvre, work out how long the NERV would need to burn to complete it, add the two times together and divide by two to get a time for starting the burn.

Unfortunately this doesn't seem to work; I must be missing something but I'm danged if I can see what.  Can someone point me in the right direction here?  I suspect I'm being really stupid, but I just can't figure this one out.

Thanks everyone.

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@The Flying Kerbal Have you considered... not staging during the burn?  I know this isn't strictly what you're asking for, but it does get around your problem.

"Periapsis kicking" is a strategy usually employed for handling burns that are so long that they cannot be reasonably completed in one pass - usually because the craft is using NERVs or Dawns. You split the burn into multiple smaller burns, first raising the apoapsis over multiple passes until the remaining dV cost to escape is so small that you can pull it off in one go.

In your case, low thrust is not your problem. But you can still use your Swivel stage to raise your apoapsis with what fuel it has, then loop around once, and perform a second burn with your NERV stage that takes you to your destination.

1.) Figure out how much dV your Swivel stage has
2.) Plan a maneuver node that expends this amount of dV
3.) Note the time to your projected apoapsis, and double it
4.) This time, or a multiple of it, is how long ahead of your desired departure time you have to execute this node
5.) Perform the burn at a suitable time
6.) After expending your Swivel stage, jettison it and then plan a new maneuver node with your NERV stage

This strategy is valid with little to no modification for any mission profile that isn't a direct Hohmann transfer to Moho. However, two caveats apply if you raise your apoapsis past the Mun's orbit. First, you must take care not to accidentally encounter the Mun, which will ruin your trajectory. And second, if your time to loop around starts going into double-digit days, you may start to see precision issues because of Kerbin's progress on its orbit around the Sun (the elongated axis of your orbit does not turn as Kerbin follows its curved path).

And finally: I may be misunderstanding you, but your description of your rocket suggests that you may want to go back to the drawing board with it. If you have a Swivel stage that has less than 1 km/s dV with "a full tank", then that is extremely inefficient construction. A good rule of the thumb is 8 to 12 times Isp worth of dV for any stage that isn't constrained by TWR or special circumstances (lander, SSTO, etc).

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@The Flying Kerbal, here's the way I often do it.  It's not the most accurate, but it's quick and gets me in the ballpark.  Let's say we have the following scenario:

We need to perform a 1000 m/s burn.  The first stage has 400 m/s remaining and will burn for 30 more seconds.  The second stage has 1000 m/s and will burn for 120 seconds.

We must use 600 m/s out of the second stage's 1000 m/s, so we use that same ratio to ballpark the second stage's burn time:

Total burn time = 30 + 120 * 600 / 1000 = 102 seconds.

Of course the problem with this is that it assumes the second stage has constant acceleration, which it doesn't.  Thus the method underestimates the burn time.  I just bump up the result a little bit, which is usually good enough for short burns.

There is, of course, a proper mathematical way to compute the actually burn time that I can show you, but it's a lot more complicated then I'm sure most of us would ever want to do in practice.

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While the acceleration of a stage isn't constant, the propellant flow rate is (assuming we're not varying the throttle).  So we'd get the correct answer if instead of multiplying the burn time of the second stage by the ratio (Δv used / Δv total), we multiplied it by the ratio (propellant used / propellant total).  We probably also need to add in a few seconds for staging, therefore the equation becomes

Total burn time = burn time remaining in 1st stage + staging time + (total burn time of 2nd stage * (propellant used / propellant total))

or expressed another way,

Total burn time = burn time remaining in 1st stage + staging time + (2nd stage propellant used / propellant flow rate)

So the trick becomes computing how much second stage propellant we're going to burn.  While the math isn't necessarily difficult, it does requires looking up more information than the quick and simple method I showed in my first post.  The equation is,

mp = mo - mo / EXP( Δv / (Isp * 9.80665) )

where mp is the mass of propellant used, mo is the total starting mass, Δv is the change in velocity, and Isp is the specific impulse.

Edited by OhioBob

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-Is it a really, really long burn?  If your burn takes so long that you're pretty far from the node by the time you start/finish it, you will lose efficiency (i.e., you will not accrue delta-v towards your maneuver as fast as your rocket loses it).  But if it's burn of a few minutes or less, this should not have a meaningful effect.

-Putting aside that issue for a moment, it should be possible to calculate burn time in this manner by using the TWR (i.e., acceleration) produced by each engine.   Of course, the TWR of both stages increases as they burn fuel, so you can't just divide the maneuver m/s by your acceleration at any given moment in time.  Sounds like a problem that could be solved with calculus - plot the acceleration over time, and see when the area under the curve equals the delta-v of your burn.

-As a practical solution, your method sounds right.  Your Swivel time is fixed based on fuel remaining.  Your NERV time should be whatever it takes to do the portion of the burn remaining at that point.

-If it's feasible, you could try splitting the burn into two passes.  I.e., start with the Swivel stage, splitting the total burn time before/after the node as usual.  Then, on the next pass around, set up a new maneuver at the same point in your orbit  with the NERV, for whatever portion of the maneuver the Swivel did not accomplish.  This may or may not be useful for gameplay purposes, but it should at least give you clear information about the total burn time required.

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10 hours ago, The Flying Kerbal said:

add the two times together and divide by two [...] Unfortunately this doesn't seem to work

You will get much better results if you split your burn such that you do equal  work (that is, similar amounts of dV) on either side of the node. That's the original idea, btw, it's just that "equal time on either side" is easier to figure out and usually works well enough.

Or just draw two maneuvers, one for the high-power stage and one for the remaining dV from the nuke. Setting this up will be a piece of work, though, even with tools like Precise Node. I wouldn't even try it with the stock toolbox.

I cannot guarantee that either approach will work for you. You may have the generic problem of doing a low-TWR interplanetary transfer (hard to tell without knowing TWRs and burn times required for your maneuver). In that case, other methods and workarounds will be needed. Search the forum for "periapsis kick" and "split burn", there ought to be lots of tutorials.

Edited by Laie

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Keep in mind that burn time is a function of not only delta v but also acceleration. Delta v requirements will be the same for any engine but the acceleration will not. To find the starting acceleration, take the thrust that the engine produces, and divide by mass*9.81 (close to Kerbin's surface, other values entirely on and around other bodies). Now take the delta v you need and divide by the acceleration you just calculated to get burn time in seconds (actual burn time will be lower as the spent fuel means less mass and higher acceleration but for ballpark figures it'll work). So:

Know or calculate how much dv the first of the two stages will give you and for how long the engine will burn before the fuel is spent.

Calculate the burn time for the 2nd of the two stages to give you the remaining m/s.

Total burn time will be the sum of these 2 burn times. Add then the time you need for a clean separation.

Edited by LN400

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Thanks for the response everyone.  Actually splitting the burn in two sounds like a perfectly simple and sensible solution, can't think why I didn't come up with that one.

The calculation I made was based on an equation somewhere on this forum which says Time=Mass/Thrust*Delta V change.  So what I did was deduct the amount of Dv the stage with the swivel engine stage would contribute from the total, and then apply the equation to figure out the length of time the NERV would need to burn to complete the manoeuvre.  Then I added the times both stages would be running, and divided this by two to find how when I would need to ignite my first stage.

5 hours ago, Streetwind said:

@The Flying Kerbal Have you considered... not staging during the burn?

Yes I have, but I seem to run into trouble if I rely on the NERV to do the Eve transfer, mid course correction (if necessary), insertion, GIlly transfer and landing... oh and not to forget the two burns to dip and then lift the Pe into and out of the Eve atmosphere when I'm deploying the Eve lander.    Such a series of burns should be possible with the amount of liquid fuel I take send up to power the NERV (I use a tank with no oxidiser so I'm not carrying unnecessary dead weight), but somewhere I must be making a mess of something, and so far this has eluded me.

5 hours ago, Streetwind said:

@The Flying Kerbal And finally: I may be misunderstanding you, but your description of your rocket suggests that you may want to go back to the drawing board with it. If you have a Swivel stage that has less than 1 km/s dV with "a full tank", then that is extremely inefficient construction. A good rule of the thumb is 8 to 12 times Isp worth of dV for any stage that isn't constrained by TWR or special circumstances (lander, SSTO, etc).

Yes, sorry I've managed to mislead you... while I'm at work right now (and really shouldn't be typing this! ) and don't have the figures available, my swivel stage definitely has more than 1KM/s of Dv.  However the rough guide of 8 to 12 times Isp worth of Dv is new to me, so my mistake produced a gem of info!

Anyway better run along as I'm supposed to do some work for my salary and I don't think KSP would qualify in the strange place I work.  I appreciate everyone's replies, thanks very much for all the help.

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42 minutes ago, The Flying Kerbal said:

Yes, sorry I've managed to mislead you... while I'm at work right now (and really shouldn't be typing this! ) and don't have the figures available, my swivel stage definitely has more than 1KM/s of Dv.

Oh, alright. Somewhere I made the assumption that you're talking about your initial ejection burn from Kerbin towards your destination. Going back, your question indeed was asked more generally, so the burn during which you want to stage is probably not the ejection burn, but one later on.

45 minutes ago, The Flying Kerbal said:

Yes I have, but I seem to run into trouble if I rely on the NERV to do the Eve transfer (...) Such a series of burns should be possible with the amount of liquid fuel I send up to power the NERV (...), but somewhere I must be making a mess of something

The typical "mess-making" with NERV engines is exactly the kind of thing periapsis kicking is designed to counter. It is possible that with low-thrust propulsion, your ejection burn from Kerbin is so long that you go an entire half of an orbit around Kerbin while performing it. In such a scenario, you're burning massively off prograde for the majority of time, first bending your trajectory away to the left and then bending it back to the right. Both times you're spending extra fuel to do the deflections, and because there is time in between them, you also introduce an error to your final trajectory... which costs more fuel to fix later, and usually also makes your capture burn at the destination more costly.

This inefficiency exists technically at any time that your change in velocity for a maneuver is not instant and perfectly located on top of the node. But for most burns, it is inconsequential, because its magnitude is in the same neighborhood as the margin for error of your human ability to correctly pilot the spacecraft (reaction time, precision of steering inputs, etc). Only when your TWR drops low, and your parking orbit is relatively tight, does it become a problem that registers. But if you let it become really bad, it can grow to arbitrary proportions - you can get into a situation where your burn is literally impossible to finish.

Countermeasures: assuming a higher parking orbit and/or periapsis kicking.

Of course, it's merely a guess of mine that this may be what is screwing up your plans, but it's definitely something to keep an eye out for.

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My solution for 'staging during a burn' and having the mis-matching TWRs mess with the burn timing is simple:

Set your engines so that the first stage has the same TWR at burnout as the second stage has at ignition.  I use the MJ dV readout to tell me my TWRs, so it is a simple matter of sliding the thrust-limiter on the soon-to-be-discarded engine so that the TWRs lineup.  From there you just do your burn until the first stage is empty, decouple and light the second engine as fast as reasonable, and maintain much of the accuracy of the original node that was plotted.

Yes, you are purposefully reducing the thrust of the first part of the burn... but gaining a ton of accuracy(?), or at least simplicity in the process.

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If you're using KER it includes "time to burn" tools. I'm pretty sure it's smart enough to know that your first engine will run out of fuel midway and do the calculations including a second engine.

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5 hours ago, The Flying Kerbal said:

The calculation I made was based on an equation somewhere on this forum which says Time=Mass/Thrust*Delta V change.

This may be the issue.   That equation looks fine,  but as mentioned above,  mass is not constant during the duration of a burn because of fuel consumption.   So if you run the equation with your starting mass,  it will overstate the time needed for the burn.

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On 10/31/2017 at 7:48 PM, The Flying Kerbal said:

Something that's often puzzled me is if there's a calculation to figure out how long it will take to complete a manoeuvre if I need to use two separate stages to make the burn?

Well, you could use @Snark's Better Burn Time, which takes staging mid-burn into account.  Just create the node as you normally would.  BBT will notice if you'll need to stage during the burn and will take into account the use of both stages.

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13 hours ago, Geschosskopf said:

Well, you could use @Snark's Better Burn Time, which takes staging mid-burn into account.  Just create the node as you normally would.  BBT will notice if you'll need to stage during the burn and will take into account the use of both stages.

Welllll... actually not as such.    BetterBurnTime actually doesn't cope with staging in its predictions at all.  It's "mathematically accurate but mechanically simple-minded":  it simply assumes that "all fuel in the ship is to be used in the current stage" and "whatever engines are currently active are the only engines".  So it wouldn't help with predicting how long a two-stage burn will take before you start the burn, if the stages have very different TWR.

It does immediately readjust itself after you stage.  For example, if you have a high-TWR stage followed by a very low-TWR stage (like the OP's described situation in this thread), then before you do your burn, it would show an unrealistically low (i.e. optimistic) burn time based on the high TWR of the current stage-- and perhaps even give you a "not enough fuel to make the burn" warning as well, depending on the dV involved.  The instant you hit the "stage" button, it would immediately recalculate and adjust the burn-time estimate upwards.

The reason that BBT doesn't try to handle staging at all is that it's hard.  Not all that mathematically hard-- it's just the Tsiolkovsky rocket formula, anyone with a pocket calculator or a spreadsheet could work out the answer fairly simply.  But it's algorithmically hard, because of the myriad ways it's possible to set up a spacecraft's staging sequence, fuel flow, etc.  It's a really hard programming problem, and would require code that's enormously more complex than BBT (and probably would still get "outsmarted" sometimes by unusual configurations).  It's a bigger programming job than I felt like taking on, so I didn't even try.

I don't happen to use KER myself, but my understanding is that it does take staging into account, so that may be a possibility.  (KER is vastly, hugely more complex than BBT is.  It's much more code.  I'm not gonna try to "make another KER", I figure that's what KER is for.)

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20 minutes ago, Snark said:

It does immediately readjust itself after you stage.  For example, if you have a high-TWR stage followed by a very low-TWR stage (like the OP's described situation in this thread), then before you do your burn, it would show an unrealistically low (i.e. optimistic) burn time based on the high TWR of the current stage-- and perhaps even give you a "not enough fuel to make the burn" warning as well, depending on the dV involved.  The instant you hit the "stage" button, it would immediately recalculate and adjust the burn-time estimate upwards.

Well, in practice, it gives a very strong impression of taking staging into account.  At least if the rocket is arranged simply and the TWRs of the stages aren't significantly different.  Which is how I tend to build things, which is why I was thinking it was actually making the staging calculations.  Apparently there's a range of values between which you really can't tell the difference.

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4 hours ago, Geschosskopf said:

Well, in practice, it gives a very strong impression of taking staging into account.  At least if the rocket is arranged simply and the TWRs of the stages aren't significantly different.  Which is how I tend to build things, which is why I was thinking it was actually making the staging calculations.  Apparently there's a range of values between which you really can't tell the difference.

Yep, that's my own experience as well.

Where it really shows up is when you have successive stages with very different TWRs, and especially if they use different kinds of fuel.  For example, if you have an LV-N stage on top of a regular LFO stage.  Because when the LFO stage is active, BBT sees that "oh, the ship doesn't have enough oxidizer to go with the liquid fuel available", and treats all the "excess" LF (i.e. the LV-N's fuel) as dead weight, and therefore thinks that the ship's dV is limited to just the LFO stage's.  So not only will it get the burn time wrong, but it will also (falsely) say that you have nowhere near enough dV (shows the burn time in the "warning, not enough dV" format).

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37 minutes ago, Snark said:

Where it really shows up is when you have successive stages with very different TWRs, and especially if they use different kinds of fuel.  For example, if you have an LV-N stage on top of a regular LFO stage.  Because when the LFO stage is active, BBT sees that "oh, the ship doesn't have enough oxidizer to go with the liquid fuel available", and treats all the "excess" LF (i.e. the LV-N's fuel) as dead weight, and therefore thinks that the ship's dV is limited to just the LFO stage's.  So not only will it get the burn time wrong, but it will also (falsely) say that you have nowhere near enough dV (shows the burn time in the "warning, not enough dV" format).

Hmmmph.  I do this all the time (using the last bit of lifter for the start of the transfer burn) and get no complaints from BBT, nor noticably inaccurate burn times.  I think it's smarter than you give it credit for

Edited by Geschosskopf

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On ‎11‎/‎1‎/‎2017 at 4:50 AM, Streetwind said:

"Periapsis kicking" is a strategy usually employed for handling burns that are so long that they cannot be reasonably completed in one pass ...

... However, two caveats apply if you raise your apoapsis past the Mun's orbit. First, you must take care not to accidentally encounter the Mun, which will ruin your trajectory. And second, if your time to loop around starts going into double-digit days, you may start to see precision issues because of Kerbin's progress on its orbit around the Sun (the elongated axis of your orbit does not turn as Kerbin follows its curved path).

I've rarely done periapsis kicking, but when I have, this is the procedure I like:

1. Perform the first burn one day prior to the intended departure time with the maneuver node in the correct position for the next day's burn.
2. Burn until the period of the resulting orbit is exactly one day (usually about a 780 m/s burn, depending on initial orbit).
3. This will return the spacecraft to the correct location at the correct time to finish the ejection burn on the second day.

The one day orbit has a apoapsis low enough (<5700 km) that there's no fear of accidentally encountering Mun.

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